Positioning floats after next section title

Question

I am trying to allow more flexibility to the placement of figure environments.

More specifically, say that a section ends 5cm before the bottom of the page, and ends with a figure environment, which takes up 10cm of the page. The float gets pushed to the next page, and occupies the whole page. Then, the new section starts on the following page.

How can I allow the placement to be more flexible? Ideally, the float should be pushed to the top of the first page not containing a section title. This would render like so:

+-------------+-------------+-------------+
| Lorem ipsum | §2 Title    | +---------+ |
| Lorem ipsum |             | |         | |
| Lorem ipsum | Lorem ipsum | +---------+ |
| Lorem ipsum | Lorem ipsum | Fig. Abc    |
| Lorem ipsum | Lorem ipsum |             |
| Lorem ipsum | Lorem ipsum | Lorem ipsum |
|             | Lorem ipsum | Lorem ipsum |
|      1      |      2      |      3      |
+-------------+-------------+-------------+

Here is a MWE producing the un-desired output.

\documentclass{book}
\usepackage{mwe,lipsum}
\let\oldsection\section
\renewcommand\section{\clearpage\oldsection}
\begin{document}
\section{Title One}
\lipsum[1-3]
\begin{figure}[ht]
    \centering
    \includegraphics{example-image}
    \caption{Caption}
\end{figure}
\section{Title Two}
\lipsum[1-3]
\end{document}

Note that indeed, as David Carlisle suspected, I am using a \clearpage before each section. I would like to keep this behaviour as is.